5.2.4.22 Various problems on the plane

Given a trapezoid with the sum of the base lengths 18 and the sides equal to 3 and 5. The straight line \( \ell \) intersects the bases so that the area of ​​the trapezoid is divided in half and the perimeters of the two quadrangles into which the trapezoid is divided are in the ratio 8:9. Find the length of the line segment \( \ell \), the ends of which lie on the bases of the trapezoid.